Find a linear inequality with the following solution set. Each grid line represents one unit.
(Give your answer in the form \(ax+by+c>0\) or \(ax+by+c ≥0\) where \(a, b,\) and \(c\) are integers with no common factor greater than 1.)
I don't understand how to input the answer so please help clarify for me!
The correct answer is -2x + 5y + 2 > 0.
First consider the red dashed line. The y-intercept is -1. The slope is 2/1 = 2.
Therefore the equation of the line can be written as y = 2x - 1
The yellow region is below y, so the yellow region ca be expressed as y < 2x - 1
However, you are asked to exress it in the form ax + by + c >0, so subtract y from both sides of the previous equation to get 0 < 2x - y - 1
This is the same as 2x - y - 1 > 0
I've used > rather than >=, but if the yellow region is meant to include the red line then replace > by >=.